Mathematical Notes

, Volume 59, Issue 5, pp 463–476 | Cite as

Partially decomposable and totally indecomposable nonnegative matrices

  • Y. V. Bolotnikov
  • V. E. Tarakanov
Article
  • 48 Downloads

Abstract

We considerm×n (m≤n) matrices with entries from an arbitrary given finite set of nonnegative real numbers, including zero. In particular, (0, 1)-matrices are studied. On the basis of the classification of such matrices by type and of the general formula for the number of matrices of nullityt valid fort>n andt≥n>m (see [2]), an asymptotic (asn → ∞) expansion is obtained for the total number of: (a) totally indecomposable matrices (Theorems 1 and 5), (b) partially decomposable matrices of given nullityt≥n (Theorems 2 and 4), (c) matrices with zero permanent (without using the inclusion-exclusion principle; Corollary of Theorem 2).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. I. Fennet and G. Loizou, “Combinatorial aspects of rectangular non-negative matrices,”Discrete Math.,20, 217–234 (1977).MathSciNetGoogle Scholar
  2. 2.
    Yu. V. Bolotnikov and V. E. Tarakanov, “Nonnegative matrices with zero permanent,”Mat. Zametki [Math. Notes],58, No. 4, 493–504 (1995).MathSciNetGoogle Scholar
  3. 3.
    V. N. Sachkov,Probabilistic Methods in Combinatorial Analysis [in Russian], Nauka, Moscow (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Y. V. Bolotnikov
    • 1
  • V. E. Tarakanov
    • 1
  1. 1.Steklov Mathematics InstituteRussian Academy of SciencesUSSR

Personalised recommendations